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Pour bien rédiger un raisonnement par récurrence, le plus important est de rendre visible la logique de la preuve. On vérifie d’abord P₀. Puis on fixe un entier k, on suppose Pₖ vraie et on utilise cette hypothèse pour démontrer Pₖ₊₁. Écrire explicitement ce que signifient Pₖ et Pₖ₊₁ aide surtout à voir ce qui doit être transformé entre les deux rangs et où intervient réellement l’hypothèse de récurrence. Si la propriété commence à un rang n₀ plutôt qu’à 0, on initialise simplement en n₀ et on r
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